Recently, a biodiesel fuel (BDF) such as long-chain fatty acid methyl ester derived from a recyclable lipid has been attracted attention as recyclable clean energy. The most common method presently used for producing a biodiesel fuel is a transesterification method using an alkaline catalyst. However, the alkaline catalyst method has a problem in that the generated ester compound contains unreacted methanol and alkali metals (e.g., potassium or sodium) and a by-product such as free glycerin. To overcome this problem, purification by washing with water (for example, Patent Document 1) is generally performed. However, in this method, high cost and large energy are required for treating wastewater. In the circumstances, it has been desired to develop a method for producing a biodiesel fuel completely preventing or greatly reducing generation of wastewater.    Patent Document 1: JP Patent Publication (Kokai) No. 10-182518A (1998)